Middle School

Tom is 6 feet tall. If Tom stands 30 feet from the base of an apple tree looking up at an apple in the tree at an angle of sight of 48°, how far is the apple from the ground?

A. 25.6 feet
B. 27.8 feet
C. 33.2 feet
D. 38.8 feet

Answer :

Using the concept of Trigonometry, the distance of the apple from the ground would be 38.8 feets.

Using Trigonometry : SOHCAHTOA. ;

Tan θ = opposite / Adjacent

Tan(48) = x / 30

Cross multiply

30 × Tan(48) = x

x = 33.32 feets

Initial height of Tom = 5.5 feets

Distance of apple from ground = x + initial height

33.32 + 5.5 = 38.82 feets

Hence, the most appropriate option is D.

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Answer:

D. 38.8 feet.

Step-by-step explanation:

Let the height of the apple be x + 5.5 feet.

Then tan 48 = x / 30

x = 30 tan 48

x = 33.3 feet.

So the height of the apple = 33.3 + 5.5

= 38.8 feet.

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